A semiconductor package may comprise a semiconductor chip, an encapsulation body encapsulating the semiconductor chip, and electrical contact elements connected with the semiconductor chip and extending through the encapsulation body in an outward direction. The electrical contact elements can be formed in a different way for serving different desires or requirements on the customer's side. According to one variant the semiconductor package is formed as a through-hole device in which the electrical contact elements are formed as contact pins to be inserted in through-hole sockets on the customer's side. According to another variant the semiconductor package is formed as a surface mount device in which the electrical contact elements are formed with flat coplanar lower surfaces to be attached on a suitable contact surface on the customer's side. For the fabrication of semiconductor chip packages and their electrical contact elements other aspects have to be taken also into consideration. One aspect may be that the semiconductor chip may produce heat during operation and the complete design of the semiconductor chip package may have to be optimized to facilitate most efficient heat dissipation. Another aspect concerns the fabrication process of the semiconductor chip package, in particular the problem of how to increase the leadframe density in the fabrication process and thereby to decrease the fabrication costs per each semiconductor chip package.